Besides this case we intend to treat other cases
of Shimura's list.
But one may decide to go further into unknown territory
and count for other families
of curves not closely related to Shimura varieties.
One obvious case are the families \({\mathcal {H}}_{g}\)  of
hyperelliptic curves of given \(g\)  and their variants \({\mathcal {H}}_{g,n}\) . Here
the case of characteristic 2 plays a special role. Bergström gives
in [1]} recursive formulas in the genus
for the equivariant number of points of \({\mathcal {H}}_{g,n}\)  over a fixed finite field.
This reduces the problem for fixed \(n\)  to the cases of low genera.
We refer to [1]} for more details.
